grouping first (left column) and last (right column) of consecutive sequence of a Nx2 matrix

You haven't clearly defined what consecutive values means mathematically. I'm assuming a difference of 1. Also you haven't explained if both columns are to be considered independently (and what happen if values are consecutive in one column and not the others). I'm assuming that both columns have the exact same pattern so we can ignore column 2 for finding consecutive values.

A=[100 200; 101 201; 102 202; 300 400; 801 901; 802 902];

%finding start and end of consecutive runs. Only using 1st column for that
transitionrows = find(diff([-Inf; A(:, 1); +Inf]) ~= 1);  %not consecutive when difference is not 1
startseqrows = transitionrows(1:end-1);  %start row of consecutive run
endseqrows = transitionrows(2:end) - 1;  %end row of consecutive run

B = [A(startseqrows, 1), A(endseqrows, 2)]